On some representations of sample variance

The usual formula for variance depending on rounding off the sample mean lacks precision, especially when computer programs are used for the calculation. The well-known simplification of the total sums of squares does not always give benefit. Since the variance of two observations is easily calculated without the use of a sample mean, and the variance of a sample of n observations is the average of the variances of observations based on n(n-1)/2 distinct subsets of units of size 2 from the sample, it is argued that this sense of pairing may result in precision. Some other forms of variance are presented which provide some insight into it. The contribution of a new observation of variance is highlighted, which is important in sequential sampling. Notions are illustrated with examples.